The Applicants are aware of various models which have been proposed for facilitating the detection of hydrocarbons in a rock formation. So, for example, in U.S. Pat. No. 4,534,019 to Wiggins, et al and corresponding European Patent Application No. 83300227.2, a method is proposed for determining the reflectivities of shear waves (s-waves), of geologic formations. However, a problem with this method is that data representative of the presence of hydrocarbons in the geologic formation cannot be obtained directly.
Also, in recent times, variation of amplitudes of reflected compressional longitudinal waves (p-waves) as a function of the angles of incidence (or offset) has received much attention. The majority of recent publications on this subject have included some form of forward modelling in which the amplitudes of reflections in a common mid-point (CMP) gather are compared to those predicted by a model (see, for example, in this regard Ostrander, W.J.; "Plane-wave Reflection Coefficients for Gas Sands at Nonnormal Angles of Incidence"; Geophysics, Volume 49, 1984, pp1637-1648; Gassaway, G.S., and Richgels, H.J., SAMPLE: "Seismic Amplitude Measurement for Primary Lithology Estimation": 53rd Annual International SEG Meeting, September 1983, Las Vagas; Abstract Book, pp610-613; Yu, G., "Offset-amplitude Variation and Controlled-Amplitude Processing" Geophysics, Volume 50, 1985, pp2697-2708.). The modelling is generally done using the Zoeppritz equations or some simplified version thereof. However, a problem with this system is that it is very time-consuming and complicated. Also it does not give a direct indication of the presence of hydrocarbons in the rock formation.
An alternative approach is to use curve fitting techniques to invert the seismic traces to a physical model directly. The principle of this method is outlined by Stolt, R.H., and Weglein, A.B.; "Migration and Inversion of Seismic Data", Geophysics, Volume 50, 1985 pp2458-2472. Stolt and Weglein use wave equation analysis to show that the extraction of elastic parameter changes from reflection seismic data is obtained by a set of weighted stacks. However, the shortcoming of this paper is that no mention is made of how the weighting factors are obtained.